Low calcium alkali-activated cement composite or geopolymer concrete has been known for more than four decades. Although this material is used in buildings, reservoirs, railroads and other constructions, its long-term properties are little known. The aim of this study was to experimentally determine creep and shrinkage properties of plain geopolymer concrete and carbon fiber reinforced geopolymer concrete. The creep properties of the specimens were determined by loading them with 20% of ultimate stress value. The specific creep of geopolymer concrete was in the same range as ordinary Portland cement—0.00065 (1/MPa). Moreover, specimens for shrinkage deformation measurements were placed to get shrinkage deformation. Also, new information concerning a geopolymer concrete specimen’s modulus of elasticity variation in time was determined. The modulus of elasticity reached on average 32.03 GPa on day 30, 36.29 GPa on day 62 and 45.73 GPa on day 158 following the production of plain geopolymer concrete specimens and 30.12 GPa on day 30, 37.79 GPa on day 62 and 53.35 GPa on day 158 following the production of carbon fiber reinforced geopolymer concrete specimens.